Fregoli Delusion

A rare neurological condition in which the patient believes that several other people are, in fact, the same person in disguise, or all look like the same person. Part of a larger group of delusional misidentification disorders, in which the patient experiences a disjunction between the actual identity of persons, places or things, and their perceived identity. Capgras syndrome, in which loved ones are believed to have been replaced by impostors, is another member of this group of disorders.

From Wikipedia:

[This group of disorders] is usually considered to include four main variants:

• The Capgras delusion is the belief that (usually) a close relative or spouse has been replaced by an identical-looking impostor.
  
• The Fregoli delusion is the belief that various people the believer meets are actually the same person in disguise.
  
• Intermetamorphosis is the belief that people in the environment swap identities with each other whilst maintaining the same appearance.
  
• Subjective doubles,... in which a person believes there is a doppelgänger or double of him or herself carrying out independent actions.

However, similar delusional beliefs, often singularly or more rarely reported, are sometimes also considered to be part of the delusional misidentification syndrome. For example:

• Mirrored self-misidentification is the belief that one's reflection in a mirror is some other person.
  
• Reduplicative paramnesia is the belief that a familiar person, place, object or body part has been duplicated. For example, a person may believe that they are in fact not in the hospital to which they were admitted, but an identical-looking hospital in a different part of the country, despite this being obviously false.
  
• Syndrome of delusional companions is the belief that objects (such as soft toys) are sentient beings.
  
• Clonal pluralization of the self, where a person believes there are multiple copies of him or herself, identical both physically and psychologically.